ANALYTIC PROPERTIES OF THE QCD RUNNING COUPLING-CONSTANT AND TAU-DECAY

A non-perturbative expansion method which gives a well-defined analyti c continuation of the running coupling constant from the spacelike to the timelike region is applied to the inclusive semileptonic decay of the tau-lepton. The method allows us to evaluate R(tau) by integration over the non-perturbative physical region, rather than by using Cauch y's theorem, and hence to incorporate threshold effects in a very dire ct way. Within our framework the difference between the effective coup ling constants in the timelike and spacelike domains can be substantia l and is not simply a matter of the standard pi(2) terms.